Do both of you have any money I can borrow?
This is not grammatically incorrect. However, you would be asking if Person 1 AND Person 2 both have money for you to borrow. The "correct answer" is assuming that you don't need both people to lend you money.
Do either of you have any money I can borrow?
Given the situation, this logically makes more sense, as you would now be asking if one of Person 1 OR Person 2 have money. In order for you to borrow money, you only need one of them to lend you it.
First off, the correct preposition is "from." There seem to be few rules that determine which prepositions are correct, or, if there are rules, they are riddled with exceptions. The closest I can come to a justification is that the context implies a conversation, with comments coming from multiple "directions," where "directions" is a buried metaphor meaning different individuals. We commonly use "from" and "to" with directions.
Second, the plural "comments" seems far more natural than "comment" though both are grammatical. The reason is that what is usually contemplated is that more than one comment is expected and permitted. That is what distinguishes the example of "any comments" from "any doctor," where it is not contemplated that someone is going to sample the views of multiple doctors. In other words, what determines whether to use the singular or plural is not grammar, but rather intended meaning.
Finally, both sentences strike me as somewhat awkward, but this may be a purely personal reaction. I very much doubt that the speaker will appreciate any comment whatsoever. For example, the comment "You are a blithering idiot" will seldom be appreciated by the person soliciting comments.
Here is what is probably intended
I would appreciate your comments if you have any that are worthwhile and polite
which would usually get shortened to
I'd appreciate your comments
with the conditional implied by the use of the contraction of "would."
Best Answer
Either of your suggested sentences could be correct, depending on the context. If there are exactly two problems or things to be checked, that is if "them" consists of exactly two items, then "either" would be correct. If "them" consists of more than two items, "any" would be correct.
While "any" can be used for a group of two, it usually isn't so used.
Strictly speaking, "either" means "one or the other", that is, it indicates a choice of exactly one of two things. "You may either go or stay." and so the use of either suggests that there is no chance of both things being not correct. One could say
But this is a bit on the formal side, and where it is clear that "both" is possible, it could be omitted and implied.
It should be "either of them is". Because either indicates a choice of one option, it takes singular forms. It should also be "any of them is.
As the this post about the use of "each" says, singular forms should be used here, although most people will not strongly object to the incorrect plural forms. While "them" represents a group, "either", "any" (and "each" not used in the question) consider the members of that group one at a time, so singular forms are correct, and plural forms are not.
"Any of them" can be thought of as short for "any one of them" or "any one or more of them". Therefore one should say:
One should not say: "If any of the answers are incorrect..."
Another acceptable alternative would be: